How to add duplicate units of a mesh to unwrapped UV sphere
It's not very clear what you want to achieve could you clarify the animation part?

UV unwrapping is made for the purpose of texturing alone, no geometry animation is possible through unwrapping.

Do you wish to make some sort of morphing animation transitioning from the plane shape into a sphere shape?

For the duplication part try looking into dupliverts here https://www.blender.org/manual/editors/3dview/transform/duplication/dupliverts.html